Integrated structural analysis tool using linear matching method part 1 : Software development

A number of direct methods based upon the Linear Matching Method (LMM) framework have been developed to address structural integrity issues for components subjected to cyclic thermal and mechanical load conditions. This paper presents a new integrated structural analysis tool using the LMM framework for the assessment of load carrying capacity, shakedown limit, ratchet limit and steady state cyclic response of structures. First, the development of the LMM for the evaluation of design limits in plasticity is introduced. Second, preliminary considerations for the development of the LMM into a tool which can be used on a regular basis by engineers are discussed. After the re-structuring of the LMM subroutines for multiple CPU solution, the LMM software tool for the assessment of design limits in plasticity is implemented by developing an Abaqus CAE plug-­in with graphical user interfaces. Further demonstration of this new LMM analysis tool including practical application and verification is presented in an accompanying paper

Verification of the linear matching method for limit and shakedown analysis by comparison with experiments

The Linear Matching Method (LMM), a direct numerical method for determining shakedown and ratchet limits of components, has seen significant development in recent years. Previous verifications of these developments against cyclic nonlinear finite element analysis have shown favourable results, and now this verification process is being extended to include comparisons with experimental results. This paper presents a comparison of LMM analysis with experimental tests for limit loads and shakedown limits available in the literature. The limit load and shakedown limits were determined for pipe intersections and nozzle-sphere intersections respectively, thus testing the accuracy of the LMM when analysing real plant components. Details of the component geometries, materials and test procedures used in the experiments are given. Following this a description of the LMM analysis is given which includes a description of how these features have been interpreted for numerical analysis. A comparison of the results shows that the LMM is capable of predicting accurate yet conservative limit loads and shakedown limits

Integrated structural analysis tool using linear matching method part 2 : Application and verification

In an accompanying paper, a new integrated structural analysis tool using the LMM framework for the assessment of design limits in plasticity including load carrying capacity, shakedown limit, ratchet limit and steady state cyclic response of structures was developed using Abaqus CAE plug-­‐ins with graphical user interfaces. In the present paper, a demonstration of the use of this new LMM analysis tool is provided. A header branch pipe in a typical AGR power plant is analysed as a worked example of the current demonstration and verification of the LMM tool within the context of an R5 assessment. The detailed shakedown analysis, steady state cycle and ratchet analysis are carried out for the chosen header branch pipe. The comparisons of the LMM solutions with the results based on the R5 procedure and the step-­‐by-­‐step elastic-­‐plastic FEA verify the accuracy, convenience and efficiency of this new integrated LMM structural analysis tool

The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting

The ratchet boundaries and ratchet strains are derived for the Bree problem and an elastic perfectly plastic material with different yield stresses on-load and off-load. The Bree problem consists of a constant uniaxial primary membrane stress and a cycling thermal bending stress. The ratchet problem with differing yield stresses is also solved for a modified loading in which both the primary membrane and thermal bending stresses cycle in-phase. The analytic solutions for the ratchet boundaries are compared with the results of deploying the linear matching method (LMM) and excellent agreement is found. Whilst these results are of potential utility for purely elastic-plastic behaviour, since yield stresses will often differ at the two ends of the cycle, the solution is also proposed as a means of assessing creep ratcheting via a creep ductility exhaustion approach

Calculation of a lower bound ratchet limit part 1 – Theory, numerical implementation and verification

It is important to be able to calculate the ratchet limit of a component when performing integrity assessments of plant components. This paper details the addition of a lower bound ratchet limit calculation to the Linear Matching Method. The extension of Melan's theorem into the alternating plasticity region is explained, followed by its implementation into the Linear Matching Method calculation procedure. Finally, the convergence properties of this method are analysed by the analysis of a plate with a central hole subject to cyclic thermal and mechanical loadin

Development and implementation of the Abaqus subroutines and plug-in for routine structural integrity assessment using the linear matching method

In recent years the Linear Matching Method (LMM) has been developed as a tool for structural integrity assessments of components subjected to cyclic loading conditions. Its capabilities include, among others, calculation of the shakedown limit, ratchet limit, plastic strain range for low cycle fatigue, creep rupture time and fatigue creep interaction. The LMM is now incorporated into EDF Energy’s R5 research program for the high temperature assessment of structural components. The purpose of this paper is to describe the development of the LMM framework, its incorporation into Abaqus and current plans to take the method from being primarily research based into wider use by industry for routine structural assessments. The LMM calculations are primarily carried out using the UMAT subroutine, and the first topic discussed in this paper is the implementation of this user subroutine. This includes details of the coding scheme to allow use of multi-processors for the calculations. A brief comparison of the LMM with full cyclic FEA is also included to validate the method and to demonstrate its advantages. The second topic of this paper discusses the development of an Abaqus/CAE plug-in to aid wider adoption of the LMM as an analysis tool for industry. The structure of the plug-in is described alongside the processes used for data collection from the user and automatic configuration of the model

Linear matching method on the evaluation of cyclic behaviour with creep effect

This paper describes a new Linear Matching Method (LMM) technique for the direct evaluation of cyclic behaviour with creep effects of structures subjected to a general load condition in the steady cyclic state. The creep strain and plastic strain range for use in creep damage and fatigue assessments, respectively, are obtained. A benchmark example of a Bree cylinder subjected to cyclic thermal load and constant mechanical load is analysed to verify the applicability of the new LMM to deal with the creep fatigue damage. The cyclic responses for different loading conditions and dwell time periods within the Bree boundary are obtained. To demonstrate the efficiency and effectiveness of the method for more complex structures, a 3D holed plate subjected to cyclic thermal loads and constant axial tension is analysed. The results of both examples show that with the presence of creep the cyclic responses change significantly. The new LMM procedure provides a general purpose technique for the evaluation of cyclic behaviour, the plastic strain range and creep strain for the creep fatigue damage assessment with creep fatigue interaction

Calculation of a lower bound ratchet limit part 2 : Application to a pipe intersection and dissimilar material join

In an accompanying paper in this issue a lower bound method based on Melan's theorem was derived and implemented into the Linear Matching Method ratchet analysis procedure. This paper presents a ratchet analysis of a pipe intersection subject to cyclic thermo-mechanical loading using the proposed numerical technique. This work is intended to demonstrate the applicability of the lower bound method to a structure commonly seen in industry and also to better understand the behaviour of this component when subjected to cyclic loading. The pipe intersection considered here has multiple materials with temperature dependent properties. Verification of the results is given via full elastic-plastic analysis in Abaqus

On the shakedown analysis of welded pipes

This paper presents the shakedown analysis of welded pipes subjected to a constant internal pressure and a varying thermal load. The Linear Matching Method (LMM) is applied to investigate the upper and lower bound shakedown limits of the pipes. Individual effects of i) geometry of weld metal, ii) ratio of inner radius to wall thickness and iii) all material properties of Weld Metal (WM), Heat Affected Zone (HAZ) and Parent Material (PM) on shakedown limits are investigated. The ranges of these variables are chosen to cover the majority of common pipe configurations. Corresponding individual influence functions on the shakedown limits are generated. These are then combined to allow the creation of a safety shakedown envelope, which can be used for the design of any welded pipes within the specified ranges. The effect of temperature dependent yield stress (in PM, HAZ and WM) on these shakedown limits is also investigated